I don't know how I've gotten this question wrong. I have to compute the distance between:
$f(t) = 2t + 3$ and $g(t) = 3t^2 -1$
Their inner product is defined as $\int_{0}^{1}f(t)g(t)dt$
So I figured the distance would be $\sqrt{(f-g,f-g)}$
Where $(f-g,f-g)$ is the inner product of f-g with itself.
I got answer answer of $\sqrt{\frac{242}{15}}$ but my book says $\sqrt{\frac{123}{10}}$ and I don't understand why. I've checked that the integral evaluates to my answer so I don't think I've made a calculation error so maybe the error is in my setup?